lean_workbook_plus_592

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $\{x,y,z\}\in \mathbb{R}$ . Determine the largest $z$ such that $x+y+z=5$ and $xy+yz+zx=3$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_592 (x y z : ℝ) (h₁ : x + y + z = 5) (h₂ : x*y + y*z + z*x = 3): x + y + z ≤ 5 ∧ x*y + y*z + z*x = 3   :=  by sorry

Source